The main result of [1]} was to identify the initial rays of the scattering diagram
\(\mathcal {D}^{\rm LV}_0\) . Namely, it was shown that the initial rays form two infinite families
associated to \(\mathcal {O}(m)\)  and \(\mathcal {O}(m)[1]\) ,
with charge \(\gamma _m=[1,m,\frac{1}{2}m^2]\)  and \(-\gamma _m\)  respectively,
emitted from the points \((m,0)\)  along the boundary, for any \(m\in {Z}\) .
Moreover, the automorphism \(\mathcal {U}^{\rm eff}(\gamma )\)  on each such ray is specified by
\(\Omega _\star (\pm k\gamma _m)=\delta _{k=1}\ ,\quad \bar{\Omega }_\star (\pm k\gamma _m)=\frac{y-y^{-1}}{k(y^k-y^{-k})}\) 
